Fed is very forgiving, but sucks endgame, so my 2nd vote went to Rebel. Some minor sweep shortcomings, but Rushes can ignore a lot of minefields, has a good minelayer and Falcons are super awesome. Plus stronger economy.

Question initially put not correctly, so that the answers you need to know on what ship list the game, and allowed to whether alliances. Also a very important factor is the richness of the galaxy...

In my opinion, if we talk about the classic ship list and normal-rich galaxy, the outsiders is a Fascist and the Empire of evil. The rest is quite playable. And easy to play of course Lizard, Solar Federation and Cyborg, because they have the economic bonus.

I rate an "easy" race as any race that can terrorize your opponents with weak ships but with little combat ability. Lizard Ground Combat Advantage, Fascist Combat advantage plus Plunder, Colonial free fighters/fighter sweep & fuel and Rebel RGA are all abilities that don't require a strong economy to pull off-- all you need are a modest set of ships to take advantage of their specials.

I agree with Fireage-- in my experience the Lizards are the easiest to play. If all else fails, you can simply resort to clan drops on enemy planets with relatively weak Reptile Class Ships. The only thing you really have to worry about are ion storms sweeping them away.

Colonials are a close second, since you don't have to worry about fuel so much and you can sweep mine fields with fighters. The only problem is that their heavy carriers are deceptively fragile, and are the weakest of the carrier races, though if you build a few and also have starbases, it's really easy to stock them full of fighters.

Third, I would vote Fascists. People underestimate what they can do, and they're a nice blend of a lot of different races. Their ability to hover over an enemy world without getting attacked is nice, and if you can't kill em with the ship itself, you can always plunder it into oblivion. Again, you don't need battleships to do this; all you need is a modest set of cloaking ships to effectively harass the enemy.

Fourth would be Rebels; like the Fascists, they have an ability to terrorize enemy worlds without fear of the planet attacking back, and have availability to the best hyperspace ship in the fleet lists. With the added bonus of the strongest carrier in the game, they're also underestimated as a strong race to contend with. Again, I stress a modest set of ships. With a bunch of hyperspacing Falcons, they can effectively terrorize the enemy without worrying too much about enemy vengeance.

I voted Colonials, I never have trouble when playing this race, I like to pick Birds to see if they can win sometime.
I have experience with Robots but it happened more than once that I stuck without Duranium and without fuel.

The hardest opponents when well played are the Crystals, the Cyborg and the Empire in this order.